There is a time-honoured tradition in statistics: whipping the data until they confess. Bullish and bearish equity analysts are equally guilty of this practice.

It would seem that statistical conclusions are merely an ex-post justification of a long-held prior belief about equity markets being cheap or overpriced. Clearly, consensus, notably among sellside analysts, is bullish. I present the bullish view before discussing a bearish counterpoint.

Who can blame the equity bullish consensus? Earnings yields – a proxy for real equity yields – stand at comfortably high levels. For example, the forward earnings yield on the S&P 500 is 8.3 per cent.

Contrast real equity yields with real bond yields: with the US Consumer Price Index at 1.7 per cent and the nominal Federal Reserve funds rate at 15 basis points, real bond yields are at -1.55 per cent.

The difference between equity and bond yields – also known as the equity risk premium – is therefore close to 10 per cent. This is way above the 4-5 per cent premium required by investors to own equity, and therefore indicative of an ultra-cheap equity market.

There are two reasons why this consensus is misguided. First, because it uses dubious metrics. It is wiser to use a long-dated real bond yield because equity is a long-dated asset.

And forward earnings yields are misleading for well-documented reasons: analysts’ earnings consensus forecasts are known to be wildly optimistic; in a bid for juicier equity and call option compensations, managers encourage their accountants to inflate earnings numbers; and earnings are partially squandered by managements as they seek to prioritise growth over profitability.

So it is probably a good idea to use dividend-based – as opposed to earnings-based – equity valuation models. Unlike earnings, dividends do not lie.

Second, because consensus disregards leverage. Profits and leverage are linked (in a deadly embrace, it turns out). If deleveraging is yet to happen, then earnings growth can only be headed south.

So what if you trust dividends more than forward earnings? In a simple dividend discount model, the real equity yield is the sum of dividend yield and real dividend growth. The S&P dividend yield is 2.15 per cent. The real dividend growth has been historically 1.25 per cent.

The real 30-year yield is 0.4 per cent. Using these numbers, the equity risk premium is now 3 per cent, less than the premium level deemed acceptable. But we are not done yet, as we have not factored leverage into our equation.

Enter Michal Kalecki, a neo-Marxist economist who specialised in the study of business cycles and effective demand. Mr Kalecki showed that profits were the sum of investments and the change in leverage.

In the current environment, the implications of this equation are clear: in G7 economies, total debt is at a record 410 per cent of GDP. And this is excluding the net present value of social entitlements and healthcare expenditures, which is larger than the total debt.

Because leverage stands at unsustainably high levels in advanced economies, it should fall substantially over the long term, affecting profits negatively.

It can be assumed conservatively that the total-debt-to-GDP ratio needs to fall by 100 per cent before the debt position becomes sustainable in advanced economies. This would bring the US back to 1995, when the profit-to-GDP ratio was 45 per cent lower.

We can value the S&P under the following scenario: dividends fall by 45 per cent over a zero-growth period of 10 years. Then they resume their real growth of 1.25 per cent per year. Again, assuming a real yield of 0.4 per cent and a required risk premium of 4.5 per cent, fair market value is only one-third of current market levels.

Leverage is hence the fly in the ointment, begging the obvious question: when does the deleveraging take place? Answering this question is tantamount to timing the next major bear market. It is, of course, futile to predict a date, but as economist Herbert Stein used to say, if something cannot go on for ever, it will stop.

It is increasingly obvious that governments will take no active step towards deleveraging unless they are under the gun. But there are institutions and mechanisms that will trigger deleveraging, namely: Basel III, the bond market, default and, rarely, courageous politicians.

Inflation can also help delever, except in economies where social entitlements are inflation-indexed.

In the short term, it is clear that central banks need to entertain the illusion of viable stock market valuations by pulling rabbits from a hat. But as high-powered money reaches ever higher levels, the probability of accidents looms large.